Pirates of the Caribbean: On Stranger Tides doesn't hit U.S. theaters until May 20. But screenwriter Terry Rossio has just turned in his script for a planned fifth installment in Disney's most lucrative film franchise.

Rossio tells THR that the still-untitled script -- his first penned without Ted Elliot, who collaborated on the first four Pirates scripts -- was delivered to Disney this past weekend. It's the initial step in putting together the key creative pieces for another Pirates film. Disney would like another installment, given the $3 billion in worldwide grosses for the first three films and the likely huge returns for the fourth movie, the first to be released in 3D.

Producer Jerry Bruckheimer has said he's in to make a fifth Pirates. And sources say Disney has made overtures to Rob Marshall, who took over directing duties on Pirates 4 from Gore Verbinski, who helmed the first three pictures, to return for another go-round (though no deal is in place for Marshall).

But they key question mark is star Johnny Depp. Will he sign on for a fifth installment in the franchise?

In an interview published in the current issue of The Hollywood Reporter magazine, Depp says he hasn't seen the new Rossio screenplay but he isn't opposed to reprising his iconic Jack Sparrow character yet again.

"It boils down to story, script and filmmaker," Depp tells THR. But the actor isn't clamoring to jump back into the puffy shirt until a little time has passed after Pirates 4. He didn't relish the brutal schedule that saw him making Pirates 2 and Pirates 3 back-to-back in order to meet studio-mandated release dates in summer 2006 and 2007, respectively.

"It's not something where I would say, 'Let's shoot it next month to get it out by Christmas 2012,'" he says. "We should hold off for a bit. They should be special, just like they are special to me."

Depp's full interview, as well as the complete backstory on the making of Pirates of the Caribbean: On Stranger Tides, are available in THR's special Cannes Film Festival issue, on newsstands now.